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Linear precoding (LP) techniques for a multiuser multiple-input-multiple-output broadcast channel is investigated and analytical results of the achievable sum capacity and error performance for zero forcing (ZF) linear precoders is presented. It is shown that the detection signal-to- noise ratio of ZF-LP can be accurately approximated by a shrinking Chi-square distribution. The symbol error rate and its achievable diversity gain of ZF-LP are given. Then, an improved linear precoder based on the minimum mean-square error (MMSE) criterion is derived. Its error performance and sum capacity are analysed and compared with that of the ZF-LP. It is shown that the MMSE-LP can achieve much better error performance and a high sum capacity than the existing ZF-LP.